Most existing telephone speech transmitted in current public networks is band-limited to 0.3-3.4 kHz. Compared with wideband speech(0-8 kHz), the narrowband speech lacks low-band (0-0.3 kHz) and high-band(3.4-8 kHz) components of sound. As a result, the speech is characterized by the reduced intelligibility and a muffled quality, and degraded speaker identification. Bandwidth extension is a technique to provide wideband speech quality, which means reconstruction of low-band and high-band components without any additional transmitted information. Our new approach considers to exploit harmonic synthesis method for reconstruction of low-band speech over the CELP coded speech. A spectral distortion measurement and listening test are introduced to assess the proposed method, and the improvement of synthesized speech quality was verified.